7道分式的乘除计算题,要快,答完加分

来源:百度知道 编辑:UC知道 时间:2024/04/28 06:55:46
⑴(x+2/x-1)* (x^2-1/x^2-4)
⑵(x^2+3x+2/x^2-3x+2)*(2x-x^2/3x+3)
⑶(a^2-b^2/2ab)*(a^2-2ab/a^2-ab-2b^2)
⑷(12xy^2/x+y)*(x^2-y^2/4xy)
⑸[(2a/3b^2)^2]*[(-b/a)^3]
⑹(x+2/2x)*(x^3-3x^2/x^2+5x+6)*(x^2+2x-3/x^3-9x)
⑺(x^2-4y^2/x+y)*(1/x^2-2xy)*(x^2-y^2/x^2+xy-2y^2)

[需过程]

⑴(x+2/x-1)* (x^2-1/x^2-4)
=((x+2)*(x+1)*(x-1))/((x-1)*(x-2)*x+2)
=(x+1)/(x-2)
⑵(x^2+3x+2/x^2-3x+2)*(2x-x^2/3x+3)
=((x+1)*(x+2)*(-x)*(x-2))?((x-1)*(x-2)*3*(x+1)
=(-1/3)x(x+2)/(x-1)
⑶(a^2-b^2/2ab)*(a^2-2ab/a^2-ab-2b^2)
=((a+b)*(a-b)*a*(a-2b))/(2ab*(a-2b)*(a+b))
=(a-b)/(2b)
⑷(12xy^2/x+y)*(x^2-y^2/4xy)
=(12xy^2*(x+y)*(x-y))/(4xy*(x+y))
=3y*(x-y)
⑸[(2a/3b^2)^2]*[(-b/a)^3]
=[4a^2/9b^4]*[-b^3/a^3]
=-4a^2b^3/9a^3b^4
=-(4/9)*1/(ab)
⑹(x+2/2x)*(x^3-3x^2/x^2+5x+6)*(x^2+2x-3/x^3-9x)
=((x+2)*x^2*(x-3)*(x+3)*(x-1))/(2x*(x+2)*(x+3)*x*(x-3)*(x+3))
=(1/2)*(x-1)/2(x+3)
⑺(x^2-4y^2/x+y)*(1/x^2-2xy)*(x^2-y^2/x^2+xy-2y^2)
=((x+2y)*(x-2y)*(x+y)*(x-y))/((x+y)*(x-2y)*x*(x+2y)*(x-y))
=1/x
主要是因式分解和约分